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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313570
details
property
value
status
complete
benchmark
2.22.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n074.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.597 seconds
cpu usage
313.128
user time
310.443
system time
2.68519
max virtual memory
3.8175108E7
max residence set size
5108960.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
313.00/291.53 WORST_CASE(Omega(n^1), O(n^2)) 313.00/291.54 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 313.00/291.54 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 313.00/291.54 313.00/291.54 313.00/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 313.00/291.54 313.00/291.54 (0) CpxTRS 313.00/291.54 (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] 313.00/291.54 (2) CdtProblem 313.00/291.54 (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] 313.00/291.54 (4) CdtProblem 313.00/291.54 (5) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] 313.00/291.54 (6) CdtProblem 313.00/291.54 (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 109 ms] 313.00/291.54 (8) CdtProblem 313.00/291.54 (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 38 ms] 313.00/291.54 (10) CdtProblem 313.00/291.54 (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 11 ms] 313.00/291.54 (12) CdtProblem 313.00/291.54 (13) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] 313.00/291.54 (14) BOUNDS(1, 1) 313.00/291.54 (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 313.00/291.54 (16) TRS for Loop Detection 313.00/291.54 (17) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 313.00/291.54 (18) BEST 313.00/291.54 (19) proven lower bound 313.00/291.54 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 313.00/291.54 (21) BOUNDS(n^1, INF) 313.00/291.54 (22) TRS for Loop Detection 313.00/291.54 313.00/291.54 313.00/291.54 ---------------------------------------- 313.00/291.54 313.00/291.54 (0) 313.00/291.54 Obligation: 313.00/291.54 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 313.00/291.54 313.00/291.54 313.00/291.54 The TRS R consists of the following rules: 313.00/291.54 313.00/291.54 exp(x, 0) -> s(0) 313.00/291.54 exp(x, s(y)) -> *(x, exp(x, y)) 313.00/291.54 *(0, y) -> 0 313.00/291.54 *(s(x), y) -> +(y, *(x, y)) 313.00/291.54 -(0, y) -> 0 313.00/291.54 -(x, 0) -> x 313.00/291.54 -(s(x), s(y)) -> -(x, y) 313.00/291.54 313.00/291.54 S is empty. 313.00/291.54 Rewrite Strategy: INNERMOST 313.00/291.54 ---------------------------------------- 313.00/291.54 313.00/291.54 (1) CpxTrsToCdtProof (UPPER BOUND(ID)) 313.00/291.54 Converted Cpx (relative) TRS to CDT 313.00/291.54 ---------------------------------------- 313.00/291.54 313.00/291.54 (2) 313.00/291.54 Obligation: 313.00/291.54 Complexity Dependency Tuples Problem 313.00/291.54 313.00/291.54 Rules: 313.00/291.54 exp(z0, 0) -> s(0) 313.00/291.54 exp(z0, s(z1)) -> *(z0, exp(z0, z1)) 313.00/291.54 *(0, z0) -> 0 313.00/291.54 *(s(z0), z1) -> +(z1, *(z0, z1)) 313.00/291.54 -(0, z0) -> 0 313.00/291.54 -(z0, 0) -> z0 313.00/291.54 -(s(z0), s(z1)) -> -(z0, z1) 313.00/291.54 Tuples: 313.00/291.54 EXP(z0, 0) -> c 313.00/291.54 EXP(z0, s(z1)) -> c1(*'(z0, exp(z0, z1)), EXP(z0, z1)) 313.00/291.54 *'(0, z0) -> c2 313.00/291.54 *'(s(z0), z1) -> c3(*'(z0, z1)) 313.00/291.54 -'(0, z0) -> c4 313.00/291.54 -'(z0, 0) -> c5 313.00/291.54 -'(s(z0), s(z1)) -> c6(-'(z0, z1)) 313.00/291.54 S tuples: 313.00/291.54 EXP(z0, 0) -> c 313.00/291.54 EXP(z0, s(z1)) -> c1(*'(z0, exp(z0, z1)), EXP(z0, z1)) 313.00/291.54 *'(0, z0) -> c2 313.00/291.54 *'(s(z0), z1) -> c3(*'(z0, z1)) 313.00/291.54 -'(0, z0) -> c4 313.00/291.54 -'(z0, 0) -> c5 313.00/291.54 -'(s(z0), s(z1)) -> c6(-'(z0, z1)) 313.00/291.54 K tuples:none 313.00/291.54 Defined Rule Symbols: exp_2, *_2, -_2 313.00/291.54 313.00/291.54 Defined Pair Symbols: EXP_2, *'_2, -'_2 313.00/291.54 313.00/291.54 Compound Symbols: c, c1_2, c2, c3_1, c4, c5, c6_1 313.00/291.54 313.00/291.54 313.00/291.54 ---------------------------------------- 313.00/291.54 313.00/291.54 (3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) 313.00/291.54 Removed 4 trailing nodes: 313.00/291.54 -'(0, z0) -> c4 313.00/291.54 -'(z0, 0) -> c5 313.00/291.54 EXP(z0, 0) -> c
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